limit question $lim_xto0(100csc^2(x)-csc^2(fracx10))$
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How can I find this limit?
$$lim_xto0left(100csc^2(x)-csc^2left(fracx10right)right)$$
Please help me to find this limit.
calculus algebra-precalculus
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
add a comment |Â
up vote
14
down vote
favorite
How can I find this limit?
$$lim_xto0left(100csc^2(x)-csc^2left(fracx10right)right)$$
Please help me to find this limit.
calculus algebra-precalculus
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35
add a comment |Â
up vote
14
down vote
favorite
up vote
14
down vote
favorite
How can I find this limit?
$$lim_xto0left(100csc^2(x)-csc^2left(fracx10right)right)$$
Please help me to find this limit.
calculus algebra-precalculus
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
How can I find this limit?
$$lim_xto0left(100csc^2(x)-csc^2left(fracx10right)right)$$
Please help me to find this limit.
calculus algebra-precalculus
calculus algebra-precalculus
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
edited Nov 3 '13 at 7:55
Rocket Man
2,128718
2,128718
asked Nov 3 '13 at 7:39
user97619
154217
asked Nov 3 '13 at 7:39
user97619
154217
asked Nov 3 '13 at 7:39
user97619
154217
154217
With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35
add a comment |Â
With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35
With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
13
down vote
accepted
Note that when $xto0$, $sin(x)sim x-fracx^36$
$$beginalignlim_xto0100csc^2(x)-csc^2(fracx10)&=lim_xto0frac100sin^2(fracx10)-sin^2(x)sin^2(x)sin^2(fracx10)\&=lim_xto0left(10sin(fracx10)-sin(x)right)timeslim_xto0frac10sin(fracx10)+sin(x)sin^2(x)sin^2(fracx10)\&sim_0left(10left(fracx10-fracfracx^310006right)-x+fracx^36right)timesleft(frac2xfracx^4100right)=33endalign$$
answered Nov 3 '13 at 10:50
user91500
12.3k946105
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
add a comment |Â
up vote
5
down vote
Hint: write $csc x=frac1sin x$, make the fractions have the same denominator, multiply and divide with $x^4$, factor the difference of squares, and use L'Hôpitals rule.
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
13
down vote
accepted
Note that when $xto0$, $sin(x)sim x-fracx^36$
$$beginalignlim_xto0100csc^2(x)-csc^2(fracx10)&=lim_xto0frac100sin^2(fracx10)-sin^2(x)sin^2(x)sin^2(fracx10)\&=lim_xto0left(10sin(fracx10)-sin(x)right)timeslim_xto0frac10sin(fracx10)+sin(x)sin^2(x)sin^2(fracx10)\&sim_0left(10left(fracx10-fracfracx^310006right)-x+fracx^36right)timesleft(frac2xfracx^4100right)=33endalign$$
answered Nov 3 '13 at 10:50
user91500
12.3k946105
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
add a comment |Â
up vote
13
down vote
accepted
Note that when $xto0$, $sin(x)sim x-fracx^36$
$$beginalignlim_xto0100csc^2(x)-csc^2(fracx10)&=lim_xto0frac100sin^2(fracx10)-sin^2(x)sin^2(x)sin^2(fracx10)\&=lim_xto0left(10sin(fracx10)-sin(x)right)timeslim_xto0frac10sin(fracx10)+sin(x)sin^2(x)sin^2(fracx10)\&sim_0left(10left(fracx10-fracfracx^310006right)-x+fracx^36right)timesleft(frac2xfracx^4100right)=33endalign$$
answered Nov 3 '13 at 10:50
user91500
12.3k946105
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
add a comment |Â
up vote
13
down vote
accepted
up vote
13
down vote
accepted
Note that when $xto0$, $sin(x)sim x-fracx^36$
$$beginalignlim_xto0100csc^2(x)-csc^2(fracx10)&=lim_xto0frac100sin^2(fracx10)-sin^2(x)sin^2(x)sin^2(fracx10)\&=lim_xto0left(10sin(fracx10)-sin(x)right)timeslim_xto0frac10sin(fracx10)+sin(x)sin^2(x)sin^2(fracx10)\&sim_0left(10left(fracx10-fracfracx^310006right)-x+fracx^36right)timesleft(frac2xfracx^4100right)=33endalign$$
answered Nov 3 '13 at 10:50
user91500
12.3k946105
Note that when $xto0$, $sin(x)sim x-fracx^36$
$$beginalignlim_xto0100csc^2(x)-csc^2(fracx10)&=lim_xto0frac100sin^2(fracx10)-sin^2(x)sin^2(x)sin^2(fracx10)\&=lim_xto0left(10sin(fracx10)-sin(x)right)timeslim_xto0frac10sin(fracx10)+sin(x)sin^2(x)sin^2(fracx10)\&sim_0left(10left(fracx10-fracfracx^310006right)-x+fracx^36right)timesleft(frac2xfracx^4100right)=33endalign$$
answered Nov 3 '13 at 10:50
user91500
12.3k946105
edited Sep 7 at 10:25
answered Nov 3 '13 at 10:50
user91500
12.3k946105
answered Nov 3 '13 at 10:50
user91500
12.3k946105
answered Nov 3 '13 at 10:50
user91500
12.3k946105
12.3k946105
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
add a comment |Â
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
I apologise for doing this again, but how did you compute the limit with the quotient to be $2x/(x^4/100)$?
– Maths Matador
Sep 7 at 10:43
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
@MathsMatador Note that we also have $sin(x)sim x$ as $xto0$.
– user91500
Sep 7 at 10:47
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
Oh I see, that makes a lot of sense now.
– Maths Matador
Sep 7 at 10:48
add a comment |Â
up vote
5
down vote
Hint: write $csc x=frac1sin x$, make the fractions have the same denominator, multiply and divide with $x^4$, factor the difference of squares, and use L'Hôpitals rule.
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
add a comment |Â
up vote
5
down vote
Hint: write $csc x=frac1sin x$, make the fractions have the same denominator, multiply and divide with $x^4$, factor the difference of squares, and use L'Hôpitals rule.
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
add a comment |Â
up vote
5
down vote
up vote
5
down vote
Hint: write $csc x=frac1sin x$, make the fractions have the same denominator, multiply and divide with $x^4$, factor the difference of squares, and use L'Hôpitals rule.
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
Hint: write $csc x=frac1sin x$, make the fractions have the same denominator, multiply and divide with $x^4$, factor the difference of squares, and use L'Hôpitals rule.
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
answered Nov 3 '13 at 8:33
detnvvp
6,7791018
6,7791018
add a comment |Â
add a comment |Â
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With these kinds of problems, the first thing I'll usually do is try breaking down CSC and any other trig functions into other trig functions that are easier to deal with. Which usually helps at leas somewhat.
– scott_fakename
Nov 3 '13 at 7:46
Try Maclaurin series
– user85798
Nov 3 '13 at 8:35